Passing a list reference to Manipulate has a different effect to passing the list verbatim

Question

I had a similar question earlier, but it was answered, and including this there would be messy.

This works: (it draws just the vertical sides of a rectangle of size 2w*2h)

Clear["`*"]
P = {};
p1[w_, h_] := {-w, -h};
p2[w_, h_] := {-w, h};
p3[w_, h_] := {w, -h};
p4[w_, h_] := {w, h};
line1[w_, h_, pt_] := Line[{p1[w, h] + pt, p2[w, h] + pt}];
line2[w_, h_, pt_] := Line[{p3[w, h] + pt, p4[w, h] + pt}];
AppendTo[P, line1[w, h, pt]];
AppendTo[P, line2[w, h, pt]];
With[{P = P}, 
 Manipulate[
  Graphics[{line1[w, h, pt], line2[w, h, pt]}, PlotRange -> 1, 
   Axes -> True], {{w, 0.5}, 0, 1}, {{h, 0.5}, 0, 
   1}, {{pt, {0, 0}}, {0, 0}, {1, 1}}]]

However if you replace the final line with this, it fails (it draws two diagonal lines).

With[{P = P}, 
 Manipulate[
  Graphics[P, PlotRange -> 1, 
   Axes -> True], {{w, 0.5}, 0, 1}, {{h, 0.5}, 0, 
   1}, {{pt, {0, 0}}, {0, 0}, {1, 1}}]]

Notice that the only difference in that line is replacing the {line1 ...} with P. If you print {line1 ...} and P, they look identical.

I think the problem is variable scope. I've tried With[{w = w, h = h, pt = pt, P = P}, ...]. Same result. I've tried removing the With[{P = P} ...]. I get an error.

The reason this is important is, I have to pass a long set of lines in P, and it's cumbersome to write them all inside the Graphics[...] statement.

Answer 1

Notice change to the very last line for the evaluation of pt inside the Manipulate:

Clear["`*"]
P = {};
p1[w_, h_] := {-w, -h};
p2[w_, h_] := {-w, h};
p3[w_, h_] := {w, -h};
p4[w_, h_] := {w, h};
line1[w_, h_, pt_] := Line[{p1[w, h] + pt, p2[w, h] + pt}];
line2[w_, h_, pt_] := Line[{p3[w, h] + pt, p4[w, h] + pt}];
AppendTo[P, line1[w, h, pt]];
AppendTo[P, line2[w, h, pt]];
With[{P = P},
 Manipulate[
  Graphics[P, PlotRange -> 1, Axes -> True], {{w, 0.5}, 0, 
   1}, {{h, 0.5}, 0, 1}, {{pt, 0}, 0, 1}]]

The reason is that you change the structure of the calculation when you enter the manipulate with pt yet unevaluated, but with the rest of the expression already evaluated using a function. Inside the manipulate, you were adding a scalar to a pair.

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To help understand what was going on, I used a few Echo statements outside and inside Manipulate for troubleshooting such as:

Echo[P, "outside "];

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That's your problem, how you intend to solve it, I leave it up to you to post your own answer when you do so.